Jesus seems to equivocate in Luke 21. How can his followers be executed and protected from death at the same time? That doesn't make sense.
Let's look closely at the passage in question. Jesus is describing the tensions that will characterize persecution later in the first century, although of course the principles hold true for all time.
Luke 21:16 You will be betrayed even by parents, brothers, relatives and friends, and they will put some of you to death. 17 All men will hate you because of me. 18 But not a hair of your head will perish. 19 By standing firm you will gain life.
Among the early Christians, the promise of protection in vv.18-19 was sometimes fulfilled literally (Acts 4:21,29; 9:23-25; 12:6-11), and other times not (Acts 12:2 etc). So life was guaranteed, though not always one's physical life.
You are right: v.18 literally (though not actually) contradicts v.16, so this clearly demonstrates that we must always strive to understand in what sense the biblical writer or speaker intended his/her words to be understood--literally or metaphorically. It is unlike Jesus (whose words are represented by Luke) would have contradicted himself after only two verses. Thus "life" (v.19) must be spiritual, not physical.
By misunderstanding the sense of biblical phrases, the majority of modern Bible-believing Bible readers imagine that faithfulness exempts us from suffering and death. "Prosperity theology" directly contradicts the message of the Cross.